Question

Solving systems by graphing and tables : equations and inequalities

Answer 1

Given,

The system of inequalitites are,

`\begin{gathered} 2x+3y>0 \\ x-y\leq5 \end{gathered}`

The graph of the inequalities is,

The are three possible solution for the inequality.

For (0, 0),

`\begin{gathered} 2x+3y>0 \\ 2(0)+3(0)>0 \\ 0>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 0-0\leq5 \\ 0\leq5 \end{gathered}`

For (3, -2),

`\begin{gathered} 2x+3y>0 \\ 2(3)+3(-2)>0 \\ 0>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 3-(-2)\leq5 \\ 5=5 \end{gathered}`

For (5, 0),

`\begin{gathered} 2x+3y>0 \\ 2(5)+3(0)>0 \\ 5>0 \\ \text{Similarly,} \\ x-y\leq5 \\ 5-(0)\leq5 \\ 5=5 \end{gathered}`

Hence, the solution of the inequalities is (5, 0).